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### Using Cancellation to Add Positives and Negatives

```Date: 10/27/2003 at 11:44:04
From: Ivette
Subject: algebra

Why is algebra so hard? What can I do to memorize formulas better?

For example, when adding numbers, I can't remember when the answer is
supposed to be positive, or when it's supposed to be negative.
```

```
Date: 10/27/2003 at 22:00:34
From: Doctor Ian
Subject: Re: algebra

Hi Ivette,

In my opinion, that's the wrong question to be asking.  Memorizing
formulas is a poor solution in the long run, because you'll forget
everything that you don't use on a daily basis--especially when you're
under a lot of stress, for example, during a test!

Whenever you find yourself trying to memorize something, that's a sign
that there's something you need to understand better.

negative numbers, keep in mind that they refer to opposite directions
on the number line.  So instead of '+this' and '-that', you can think
of them in terms of east (+) and west (-).

(Or you can use north and south, or up and down, or in and out...
whichever pair of opposites seems most natural to you.)

If I go 2 miles east, and 3 miles east, where do I end up?

2 east + 3 east = 5 east            (2 + 3 = 5)

What if I go 2 miles east, and then 3 miles west?

2 east + 3 west = 1 west            (2 + -3 = -1)

How can I see this, without memorizing it?  Well, I can break the trip
west into two parts:

2 east + 2 west + 1 west

Now the first to cancel each other out!

(2 east + 2 west) + 1 west = 0 + 1 west = 1 west

Now, we _could_ do this just using signs, instead of directions:

2 + (-3) = 2 + (-2 + -1)

= (2 + -2) + -1

= 0 + -1

= -1

But the important thing is, we can see how it works without having to
memorize any rules or formulas.

Does this make sense?

- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Negative Numbers

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